Complex numbers

[north osprey]

So I have this equation: |z + 1 - 3i| = |z - 1 + i|.
I’ve tried to solve it by replacing z = x + iy. I’m supposed to write it in the form of y = kx + m. The answer I get to is y = x + 2 but the answer sheet says y = 1/2x + 1. How do you get to that? I included how I’ve solved it. Any tips are greatly appreciated. Thanks in advance

[fresh citrus]

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[vestal leaf]

, rotate

[vestal leaf]

redo your calculations

the premise is correct

@north osprey

[velvet forge]

An advice I can give is to try to look at the problem geometrically if you have two complex numbers a and b and you want to find the complex numbers z such that |z-a|=|z-b| that basically means you want to find the complex numbers that are equidistant to a and b which is actually a line, the line must contain (a+b)/2

[vestal leaf]

(x+1)^2 + (x-1)^2 = (x-1)^2 + (x+3)^2 is not true

[velvet forge]

From this you know that the set of complex numbers that you are looking for are of the form x+iy with y=kx+m, here using the fact that (a+b)/2 is contained within the line you already have m and you can find k using some calculations

This is a bit of a different a approach looking at it geometrically but doing the calculations is good as well

[north osprey]

Ok guys thank you for the advice. I’ll try to look at it based on your comments and I’ll come back if I don’t understand

[north osprey]

It helped, thank you guys. Especially the geometric suggestion!

+close